There are some effects which trigger when damage is taken. Asana's shield, for example. These will only trigger off of direct damage. So if she puts her shield up and then runs through a Lockwood trap (which is indirect), the shield won't trigger from the trap.
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Rampart's shield is trickier. But some rules of thumb: If the ability is some kind of projectile(s) from the attacker, it will probably be blocked. If it comes from the ground, from the sky, etc, then it will probably not be affected. Anything that goes through walls will also go through Ramp's shield.

Remember Ramp's shield works in both directions, but that the shield is on the border between squares. So it will still hit things (like Rampart) on the way to the shield if it's coming from behind Rampart.

I haven't figured out a pattern to the dash moves. Some dash moves will be stopped by the shield (like PuP and Asana I think), and some dash moves can go through it (like Rask and Lockwood ult I think)

Some things that I remember surprised me: The shield blocks the prep-phase part of Zuki's ultimate. It blocks Rask's ult. Asana's dash and Lockwood's primary will bounce off the shield (instead of being stopped) just like a wall.

I haven't figured out a pattern to the dash moves. Some dash moves will be stopped by the shield (like PuP and Asana I think), and some dash moves can go through it (like Rask and Lockwood ult I think)

Titus' and Asana's dashes interact with Rampart wall because they are laser-targeted dashes on the ground which specifically terminate or bounce when they hit walls. PuP's dash actually should NOT be affected by Rampart's wall, but on inspection it appears that it is currently blocked by it. We'll fix this in the near future! The goal with Rampart's wall is to have it behave exactly as a wall would as often as possible.

The other catch there is that his ult deploys the wall during Dash phase - which means it's not up to interact with other dashes when they are activated. So for instance, you can block Titus's dagger with Rampart wall, but you *cannot* block Titus's dagger with Rampart Ult - because the wall won't be in place until after the dagger is thrown.

Titus' and Asana's dashes interact with Rampart wall because they are laser-targeted dashes on the ground which specifically terminate or bounce when they hit walls. PuP's dash actually should NOT be affected by Rampart's wall, but on inspection it appears that it is currently blocked by it. We'll fix this in the near future! The goal with Rampart's wall is to have it behave exactly as a wall would as often as possible.

The other catch there is that his ult deploys the wall during Dash phase - which means it's not up to interact with other dashes when they are activated. So for instance, you can block Titus's dagger with Rampart wall, but you *cannot* block Titus's dagger with Rampart Ult - because the wall won't be in place until after the dagger is thrown.

Ok, wait, I know it took a few days but now that I think about it this is confusing me. Rask, Lockwood and etcetera CAN'T dash through walls, nor is their damage capable of going through walls. Rask can dash over impathable cover, but not true walls. This makes the selective dash blocking even more confusing...

The only difference is in tile-selection targetting vs line-selection targetting. But that has nothing to do with walls.

His shield does not block any dashes unless the dash does something with the target (vague I know) imagine all the dashes are aimed through a stealth field:

while Titus and Asana would stop dashing if they hit an enemy in that field, Rask and Lockwood would not.
This is the same with ramparts shield:
Titus stops in front and does his spinning strike thing and Asana bounces off the shield because it's handled like a wall (Trick Shot bounces off it too)
And Rask and Lockwood just dash straight trough it.

Also important to know in my opinion:
If you block Juno's Ultimate with your shield or she sweeps into your shield the beam gets cut off for the rest of the turn: So it's still cut off after you put the shield away and the movement is handled.

As for Ramparts ultimate:
Since he dashes to the target and deploys his shield. Obviously this is handled in the DASH-phase and obviously you can't block any PREP- or DASH-phase stuff with it.
Although I haven't tried whether you can bounce Asana's dash with your's if you are faster (dash shorter) and she hit's the spot after you already deployed (if she dashed over a greater distance).

Lockwoods ult, Ramparts ult, i believe ozs ult, and rask's dash are not blocked by Ramparts wall because they do damage as they pass through an area. Imagine lockwood shooting like a madman in all directions as he runs through, so he applies the dmg once he on the other side of the wall. Their dashes are to a specific point, whereas titus and asana dash to the first thing hit applying damage from the direction they are going like a shot.
You can use this logic to apply it across everyone. The wall wont block khita from dashing to where she wants because she goes to a specific point. The damage from zuki's dash can be blocked as it comes outward from her point like any blast phase shot would. The wall blocks damage from the direction it is facing. Anything that doesn't do dmg to that direction, gets around it.

The shield as a prep phase move can be considered (as something that is rare) as a "first" and will block other prep abilities like titus' dagger and greys dart, but of course not abilities like celeste's trap because it goes under.

To my understanding it basically works as cover: If it would go through cover, it goes through shields.
It also blocks any "damage dashes": Lock ult, Oz ult, Rask dash, etc. Anyone who "shoots" with their dash (Elle, Khita) don't go through Ramp shield. Oddly, Asana dash is blocked by Ramp shield? So I assume it's any dash that hits in an AoE.

To my understanding it basically works as cover: If it would go through cover, it goes through shields.
It also blocks any "damage dashes": Lock ult, Oz ult, Rask dash, etc. Anyone who "shoots" with their dash (Elle, Khita) don't go through Ramp shield. Oddly, Asana dash is blocked by Ramp shield? So I assume it's any dash that hits in an AoE.

I works more like walls Kirby, every damage that Ignores walls also gets through the shield:
i.e. Zuki's Ultimate gets blocked by Rampart's shield and no one behind the shield becomes targeted.
However, if Zuki has the Mod that scans through wall, she also ignores ramparts shield.

Asana's Dash bounces off Ramparts shield because it would bounce off walls as well.
as for Lockwood Oz and especially Rask... their Dashes are NOT blocked by Ramparts shield, and players behind the shield still get damaged by them.

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Gracious in Defeat.
Unless you are a (!@#$%&) about it.